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Bulletin of the American Physical Society

The Molecular Hubbard Hamiltonian

Lincoln D. Carr, Michael L. Wall

Published Mar 16, 2010• 0 citations
OpenAlex

Abstract

In recent years there has been a great deal of progress towards cooling heteronuclear alkali metal dimer molecules to quantum degeneracy in their absolute ground state [1]. Ultracold polar molecules such as these are of great interest in many fields ranging from precision science and metrology to manybody physics [2]. Of particular interest to many-body physics is the fact that heteronuclear molecules have permanent electric dipole moments which give rise to long-range interactions in a DC electric field. Also, because of a nuclear quadrupole coupling, this dipole moment can also be used to access the many internal hyperfine states in a controlled way. This paves the way to rich, complex dynamics, such as the many-body dephasing of Rabi flopping between two internal states as shown in Fig. 1.

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An ultracold gas of heteronuclear alkali-metal dimer molecules with hyperfine structure loaded into a one-dimensional optical lattice is investigated. The hyperfine molecular Hubbard Hamiltonian (HMHH), an effective low-energy lattice Hamiltonian, is derived from first principles. The large permanent electric dipole moment of these molecules gives rise to long-range dipole-dipole forces in a dc electric field and allows for transitions between rotational states in an ac microwave field. Additionally, a strong magnetic field can be used to control the hyperfine degrees of freedom independently of the rotational degrees of freedom. By tuning the angle between the dc electric and magnetic fields and the strength of the ac field, it is possible to control the number of internal states involved in the dynamics as well as the degree of correlation between the spatial and internal degrees of freedom. The HMHH's unique features have direct experimental consequences such as quantum dephasing, tunable complexity, and the dependence of the phase diagram on the molecular state.
Ultracold molecules have recently attracted much attention because of their envisioned impact on both technology and fundamental science. The physics within them, i.e. their rich internal structure, and between them, i.e. long-range interactions, offer an increased complexity compared to atoms, while allowing for full experimental quantum control of the relevant degrees of freedom. A promising method of production consists of a first stage, whereby the component atoms are trapped and cooled to ultracold temperatures, and a second stage, whereby these are associated into dimers. In particular, the ability of cooling alkaline-earth (AE) elements, besides more traditional alkalis (A), has put production of AE-AE and A-AE molecules within experimental reach. Homonuclear ground-state AE-AE, because of their insensitivity to external electric and magnetic fields, have been proposed for metrology and precision measurements. In this work we investigate efficient production of Sr dimers starting from either an atomic Mott-insulator or Bose-Einstein condensate. Heteronuclear ground-state A-AE would allow for novel few-body and many-body physics experiments. In this thesis we investigate production schemes for RbSr dimers, which oweing to their large electric and magnetic dipole moments and heavy mass, are ideal candidates for the attainment of quantum degeneracy and subsequent experiments. We show our results from optical spectroscopy and combine them with thermal fluorescence data from our collaborators in Warsaw to derive the ground-state potential energy curve. Finally, we report on the experimental observation of magnetic Fano-Feshbach resonances between Rb and Sr and argue for their applicability to efficient molecule production.
Ultracold quantum gases are versatile model systems for exploring quantum physics or for the simulation of solid state materials. Meanwhile, they have been created from various atomic species - from alkali metals over alkaline earths to rare earth elements. The latest addition are quantum gases of different kinds of polar molecules. Expectations for quantum gases of heteronuclear molecules are high: Due to their large electric dipole moments, these molecules can interact with each other via long-range interactions - not just via contact interactions as is the case for most atoms. Additionally, they have vibrational and rotational degrees of freedom, with open up new possibilities for quantum simulation. But the same degrees of freedom also pose some challenges. For example, they make the preparation of the quantum gas more difficult, which is typically produced with a combination of laser cooling and evaporative cooling in the atomic case. Molecules mostly lack closed transitions in their spectra, which are required for laser cooling. Therefore, we create our molecular quantum gas from a mixture of two atomic quantum gases. In this work, such an experimental method was developed for fermionic NaK molecules, which is based on the two-photon process Stimulated Raman Adiabatic Passage (STIRAP). Within STIRAP, the hyperfine structure of the chosen intermediate state plays an important role. Experimentally, and with the help of a theoretical model describing the whole process, we find that we produce the most molecules when we use a large one-photon detuning, if the hyperfine structure of the intermediate state is unresolved. In another project, we explored the rotational level structure of the molecular ground state populated by STIRAP. Rotation is closely linked to the electric dipole moment. The superposition of the ground state with the first excited rotational state, for example, has a transition dipole moment of almost 60% of the permanent electric dipole moment. Unfortunately, coherence times of such superpositions are typically short, as the different polarizabilities of the rotational states lead to dephasing in optical traps. However, using a special polarization angle and a small, dc electric field, we can compensate these differences and realize a spin-decoupled magic trap. With this new technique we obtain record coherence times, at least for small molecular densities. For larger densities we observe first indications for dipolar interactions in a bulk gas of polar molecules, which we also model using the moving-average cluster expansion (MACE).